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My read on C(1) and C(2) is that they are not probabilities
    at all (at least I don't see a probabilistic model in use
    in this part of Mark's paper) but are simply triad counts.
As such, there are MANY different kinds/types/varieties of
    triad counts (for different types of relations) --- Steven,
    let me suggest you consult the literature on transitivity
    and clusterability (which is extensive, and generated many
    different kinds of "clustering coefficient").


Stan Wasserman



************
On Jan 12, 2005, at 11:32 AM, Mark Newman wrote:


On Wednesday 12 January 2005 11:18 am, Steven L. Johnson wrote:
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Matthew -- I think you'll find the following article really helpful:

Newman, M. E. J. (2003) "The structure and function of complex
networks,"
      SIAM Review (45) 2, pp. 167-256.
      http://epubs.siam.org/sam-bin/getfile/SIREV/articles/42480.pdf

See section 3.2 in particular (page 17 of the PDF, page 183 of the
article). Newman talks about two different clustering coefficient
formulas, which he refers to as C(1) and C(2).

Newman notes that the Watts & Strogatz definition, C(2), tends to
weight low-degree nodes more heavily than C(1).

That leads me to a follow-up question: Can anyone on the list offer
guidance as to what situations either measure is more appropriate
for??

****************

Both definitions can be described in words simply enough.  C(1) is "the
probability that two people with a common acquaintance know one
another".
(There's some subtleties about that, but that's the basic idea.)  C(2)
is
"the probability that two acquaintances of a randomly chosen person know
each other".  Thus the crucial difference is whether you are focusing on
the two people or on their common acquaintance.  One can imagine
experimental designs in which either of these two definitions might be
useful.  Where mathematical calculations are concerned, however, the
first
is almost invariably easier to calculate.

Mark Newman


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Stanley Wasserman
Sociology and Psychology
Indiana University

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http://www.indiana.edu/~appstat/
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